Migration and Business Cycle Dynamics Christie Smith 1 Christoph - - PowerPoint PPT Presentation

Migration and Business Cycle Dynamics

Christie Smith1 Christoph Thoenissen2 Treasury Guest Lecture 18 April 2018

1Reserve Bank of New Zealand 2University of Sheffield

Disclaimer

The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Reserve Bank of New Zealand

• r any other person associated with the Reserve Bank of New Zealand.

Motivation

◮ In recent years, 2015 in Europe, and 2012 onwards in New Zealand, we have seen

exceptionally large international movements of people.

◮ The recent increase in net migration has certainly had a political impact. The

question we ask in our paper is whether that impact is underpinned by observed macro effects?

◮ The economics profession has, of course, been paying attention to migration as a

phenomenon, but much of that work has tended to be focused on microeconomic and labour market effects of migration (Burstein et al 2017, NBER). Very little work has focused on the short-run macroeconomic effects of international labour mobility.

◮ For a good survey of the existing literature see Kerr and Kerr (2011, NBER) ◮ To the best of our knowledge this is amongst the first papers to analyse the role

• f migration shocks on the business cycle.

Popular perception of migration is often negative ...

... and usually orthogonal to the actual macroeconomic effects of migration.

Motivation

◮ The aim of our paper is to analyse the macroeconomic consequences of shocks to

net migration.

◮ Are the macroeconomic consequences of migration as bad as popular opinion

suggests?

◮ Surprising lack of literature on the macroeconomics of migration.

Not much [macroeconomics] literature

◮ Mandelman and Zlate (2012, JME) ‘Immigration, remittances and the business

cycle’ - Remittances help smooth consumption in Mexico. Trade in labour substitutes for trade in assets.

◮ McDonald (2013), ‘Migration and the housing market’ AN/RBNZ. Documents

the effect of arrivals versus departures on aggregate house prices.

◮ Vehbi (2016), ‘The macroeconomic impact of the age composition of migration’,

AN/RBNZ. Demand pressures of migration linked to age of migrants.

◮ Armstrong and McDonald (2016), ‘Why the drivers of migration matter for the

labour market’, AN/RBNZ. Links net current increase in migration into NZ to higher Australian unemployment rate.

Not much [macroeconomics] literature

◮ Clemens and Hart (2016, mimeo) ‘Migration, unemployment and the business

cycle’ - What determines migration flows in the Euro-area.

◮ Weiske (2017, mimeo) ‘On the Macroeconomic Effects of Immigration: A VAR

Analysis for the US’ - comes close to what we do in treating migration as a driver, but different empirical approach and for the US. Finds that migration is not a major driver. Not surprising as migration into US has been below 0.4% of labour force since 1925.

◮ Furlanetto and Robstad (2016, mimeo) ‘Immigration and the macroeconomy:

some new empirical evidence’ - Norges Bank work - a migration shock lowers unemployment, improves public finances and has a negative effect on productivity.

Objectives

◮ Two main objectives of our work: (i) understand the transmission mechanism of

a migration shock, and (ii) understand the role migration shocks in the business

• cycle. In other words, does migration actually matter for the macroeconomy?

◮ Apart from the effects of migration shocks on the usual components of GDP, we

are also interested in understanding the role of migration shocks on the residential real estate market.

◮ To answer these questions, we build a small open economy DSGE model with

migration shocks and take it to the data. First we estimate our model using Bayesian techniques.

◮ We check for the robustness of our results by using a less restrictive SVAR

approach on the same data set.

A model of migration in a small open economy

◮ Adding migration to dynamic business cycle models is relatively straight forward:

from a modelling point of view, it is simply allowing for variation in the growth rate of the working age population.

◮ Small Open Economy model → allows us to treat migration as exogenous. We

focus on the country-of-destination, not the country of origin.

◮ Economy is price taker in international goods and factor markets. Open economy

RBC model.

◮ Households use their time endowment for leisure, work, and skill accumulation. ◮ Accumulated skills/human capital differentiates migrants from ‘natural’

population increase.

A model of migration in a small open economy

◮ Economy consists of three sectors: household sector, traded goods

producing-sector, and housing sector.

◮ Firms produce domestic goods with capital, whose intensity of use they can vary,

and effective labour.

◮ Houses are built using land, effective labour, and final goods. ◮ Other useful open economy features: PPP deviations via consumption home-bias;

incomplete financial markets.

Model details: Households

◮ Households have preferences over consumption, housing, hours of work and hours

• f skill acquisition.

Ut =

• jc

t ln ct + jt ln ht −

φ0 1 + η (nt + st)1+η

• (1)

◮ Final consumption goods are an aggregate of home and foreign-produced

intermediate goods. ct =

• v

1 θ

• ch

t

θ−1

θ

+ (1 − v)

1 θ

• cf

t

θ−1

θ

• θ

θ−1

. (2)

◮ Households maximise expected utility subject to the flow budget constraint:

ct + pf

t bt + qH t ht + pl tlt = (1 + rt−1)pf t

Nt−1 Nt bt−1 + qH

t (1 − δh) Nt−1

Nt ht−1 (3) +wtnt Nt−1 Nt dt−1 + (pl

t + Rl t) Nt−1

Nt lt−1 + πt

Model details: Human capital

◮ Human capital is produced by combining existing human capital with time spent

training.

◮ The stock of human capital, denoted dt, evolves according the following law of

motion: dt = ( Nt−1 Nt dt−1st)φs N2φs−1

t

+ (1 − δd) Nt−1 Nt dt−1 (4) where (dt−1st)φs denotes the production technology that turns effective time investment into human capital and δd denotes the depreciation rate of human capital.

Household’s FOCs

Model details: Households’ interactions with firms

◮ Households supply firms with effective labour, defined as ntdt−1

Nt−1 Nt

= ent, which is remunerated with the real wage wt.

◮ The opportunity cost of investing in human capital is borne exclusively by the

household and not the firm.

◮ Households divide total effective labour, ent, between the goods producing sector,

supplying eny

t units of labour, and the construction sector, supplying enH t units of

labour. ent = eny

t + enH t

(5)

Model details: Goods-producing firms

◮ Firms maximise profits:

πy

t = ph t yt − wteny t − xt

(6) subject to a production technology that combines effective labour and utilised capital: yt = at(ut Nt−1 Nt kt−1)α(eny

t )1−α.

(7) The usual law of motion of the capital stock is defined as: kt = (1 − δ(ut))kt−1 Nt−1 Nt + ai

tι(xt/xt−1).

(8)

◮ Notable features: firms employ effective labour, can vary the degree of capacity

utilisation, and face investment adjustment costs. Migration dilutes the existing capital stock per worker.

Firms’ FOCs

Model details: Construction sector

◮ Our housing and construction sector is based on Iacoviello (2005, AER). Housing

stock is built using effective labour, land and home-produced intermediate goods, mt.

◮ Profits in the construction sector at time t are defined as πH

t , with

πH

t = qH t Ht − wtenH t − Rl tlt−1 − ph t mt

(9)

◮ New houses are produced using land, effective labour and home-produced traded

goods: Ht = aH

t (lt−1)ξl enH t 1−ξl −ξmmξm t

(10) where aH is the total factor productivity in construction.

Model details: Construction sector

First order conditions

◮ FOCs for effective hours, land usage and intermediate inputs:

(1 − ξ − ξm)qH

t

Ht enH

t

= wt (11) ξlqH

t

Ht lt−1 = Rl

t

(12) ξmqH

t

Ht mt = ph

t

(13)

◮ Market clearing implies that the supply of new houses equals the net increase in

the housing stock. Ht = ht − (1 − δh) Nt−1 Nt ht−1 (14)

Model details: Supply of building land

◮ The total supply of land is fixed, which would implies that net migration

permanently reduces the supply of land per capita.

◮ Indeed, that is the main effect of migration, it dilutes stock on a per capita basis.

This is not a problem for reproduceable stocks like human and physical capital which in the long-run return to their steady state per capita value.

◮ From a model solution point of view, we need a well-defined steady state around

which to approximate the dynamics of the model.

◮ Hence, we assume that whereas the total supply of land is fixed, the supply of

‘building land’ is allowed to grow with the population and remains constant on a per capita basis: lt = 1 (15)

Model details: Market clearing and the current account

◮ Market clearing condition for home-produced goods:

yt = v

• ph

t

−θ (ct + xt) + mt + exh

t .

(16)

◮ Export demand:

exh

t = v∗

rert ph

t

θ∗ y∗

t

(17)

◮ Current account:

yt = ct + xt + mt + pf

t bt − pf t (1 + rt−1) Nt−1

Nt bt−1 (18)

◮ Closing the model via a debt elastic interest rate:

1 + rt = (1 + r∗

t )e−φb(bt−¯ b)

(19)

Model details: Shock processes

◮ There are 7 AR(1) shocks driving the model: technology; housing technology;

‘demand’ preference shocks; ‘housing demand’ preference shocks; ‘investment-specific technology shocks’; foreign demand shocks; and migration shocks (vt).

◮ The migration process is defined as vt ≡ ln (Nt/Nt−1) ◮ Every observable has an obvious ‘driver’ e.g. GDP and TFP, Investment and MEI,

Residential Investment and jt, etc. Pretty tough for migration to have much of a

• role. . .

Migration versus population growth

◮ Migration and population growth dilute stocks on a per capita basis. Unlike

new-born locals, migrants arrive with an existing stock of human capital that may well be higher than that of locals.

◮ To illustrate the effect of migrants arriving with human capital, consider the

log-linearised evolution of dt over time: ˆ dt = φsδd ˆ dt−1 − vt + ˆ st

• + (1 − δd)
• ˆ

dt−1 − vt

• (20)

◮ Unskilled migration reduces the per capital stock of human capital in the

economy - vt reduces dt. Assume instead that migration can increase or decrease per capita human capital: ˆ dt = φsδd ˆ dt−1 − (1 − χ)vt + ˆ st

• + (1 − δd)
• ˆ

dt−1 − (1 − χ)vt

• (21)

where χ is strictly positive and takes the value of 1 when migrants possess the same level of human capital as natives, or greater than 1 when migrants have a higher average level of human capital.

Data

◮ We use quarterly data for net working-age migration, GDP, private consumption,

private investment, residential investment, real house prices and trade-weighted world GDP for New Zealand from 1992Q1 to 2017Q2.

◮ All data series are divided by working age population and, apart from migration

per capita, are logged. All series are de-trended using the filter suggested by Hamilton (2017).

◮ We focus on New Zealand, because of (a) the availability of high quality

migration data [working age migration data]; (b) because NZ has relatively large and volatile migration over the sample; and (c) migration flows into NZ have been predominantly of economically-active migrants.

◮ Very high net migration during the last 3-5 years - ca. 70k per annum –

translated to a European scale [GB or DE] that would be net migration of over 1 million per year over the last 3 - 5 years.

◮ NZ arrivals/departures predominantly via airports, hence excellent data coverage.

Filtered Data

Table: Observables and model moments

Std Dev (σ) σi/σy Corr(Yt, Yt−1) GDP per capita 0.0264 1 0.8453 Residential Investment per capita 0.1496 5.67 0.8694 Investment per capita 0.1134 4.30 0.8297 Consumption per capita 0.0275 1.04 0.8408 Real House Prices 0.1006 3.81 0.8715 World GDP 0.0164 0.62 0.8864 Migration per capita 0.0013 0.05 0.8904

Note: All data, except for net migration per capita, are in logs and and all are de-trended using the Hamilton filter.

Bayesian Estimation

◮ We match our seven data series to seven equivalent variables in the model. ◮ Two of our observables correspond directly to exogenous shock processes [World

GDP and net migration]. The AR(1) coefficient and standard deviation of their error terms of these variables are estimated using ‘tight’ priors corresponding to their actual (OLS) values.

◮ The remaining parameters have standard priors taken from the relevant literature. ◮ Bayesian estimation implemented via two MCMCs chains of 2,000,000 draws.

Table: Estimated parameters values

Parameter Description Prior Mean Std Dev

• Post. Mean

(5% 95%) α Share of capital N 0.330 0.010 0.330 0.314 0.346 αh Share of land in housing N 0.700 0.050 0.614 0.561 0.667 δ Depreciation rate capital N 2.500 0.500 2.748 1.944 3.538 η Frisch elasticity Γ 2.000 0.750 3.733 2.211 5.251 θ

• Intratemp. subst. elasticity

N 1.000 0.250 2.550 2.498 2.590 γ Openness β 0.300 0.010 0.337 0.321 0.353 acu Capacity-U curvature β 0.500 0.150 0.669 0.479 0.865 ac Investment adjustment costs N 4.000 1.500 6.313 4.433 8.131 φb × 100 Bond adjustment costs Γ−1 1.000 5.000 0.205 0.152 0.256 ρa Persistence tech. β 0.500 0.200 0.762 0.710 0.814 ρah Persistence housing tech. β 0.500 0.200 0.718 0.613 0.826 ρy Persistence foreign demand. β 0.886 0.010 0.887 0.871 0.903 ρj Persistence housing pref. β 0.500 0.200 0.860 0.806 0.917 ρjc Persistence consumption pref. β 0.500 0.200 0.830 0.780 0.879 ρi Persistence investment-specific β 0.500 0.150 0.272 0.145 0.397 ρv Persistence migration β 0.890 0.010 0.890 0.874 0.906 ǫa Std dev. tech. Γ−1 0.004 1.500 0.030 0.026 0.034 ǫh Std dev. housing tech. Γ−1 0.005 1.500 0.038 0.032 0.043 ǫyf Std dev. foreign demand Γ−1 0.007 1.500 0.007 0.006 0.008 ǫj Std dev. housing pref. Γ−1 0.005 0.500 0.535 0.335 0.728 ǫi Std dev. investment-specific Γ−1 0.005 1.500 0.366 0.244 0.483 ǫjc Std dev. consumption pref. Γ−1 0.004 1.500 0.034 0.030 0.039 ǫv Std dev. migration Γ−1 0.001 1.500 0.001 0.001 0.001 Calibrated χ Relative human cap of migrants 1.85 δh × 100 Depreciation rate housing 1 β Discount rate 1/1.01 δd Depreciation rate human cap. 0.01 φs Skill accumulation 0.5 ¯ j Steady-state j 0.7 n + s Hours worked + training 1/3 ξm Share of traded goods in housing 0.1 H/c H - C ratio 0.12

Bayesian Estimation

◮ Standard/plausible parameter estimates throughout. ◮ Migration shocks are fairly persistent with an AR(1) coefficient of 0.89, but not

very volatile with a standard deviation of 0.001.

◮ Key calibrated parameter of note is χ, the relative level of human capital of

• migrants. We follow Boubtane (2016) and choose a value of 1.85 for New

Zealand.

Figure: A migration shock in the estimated model

5 10 15 20 1 2 3 4 ×10-3 Output 5 10 15 20 0.5 1 1.5 2 2.5 ×10-3 Consumption 5 10 15 20 0.005 0.01 Investment 5 10 15 20 2 4 6 8 ×10-3 Effective hours 5 10 15 20

• 0.025
• 0.02
• 0.015
• 0.01
• 0.005

Bonds 5 10 15 20

• 5

5 10 ×10-4 Terms of trade 5 10 15 20

• 15
• 10
• 5

0 ×10-4 Wage 5 10 15 20 1 2 3 4 5 ×10-4 Migration 5 10 15 20 1 2 3 4 5 ×10-3 MPK 5 10 15 20

• 3
• 2
• 1

0 ×10-3 Housing per capita 5 10 15 20 1 2 3 ×10-3 Price of housing 5 10 15 20 1 2 3 ×10-3 Construction 5 10 15 20

• 6
• 4
• 2

0 ×10-3 Skill acquisition 5 10 15 20 1 2 3 ×10-3 Human capital

Response to a migration shock

◮ An increase in net migration is expansionary. ◮ Per capita GDP, consumption, investment, residential investment rise following

an unexpected increase in net migration.

◮ The terms of trade/real exchange rate appreciates following a net migration

shock → an appreciation is a positive wealth effect and expands output, see also Bodenstein, Kamber and Thoenissen (2017).

◮ Net migration raises the return on fixed assets, eg physical capital and housing

stock become more scarce on a per capita basis, but the return to human capital decreases, as it becomes more abundant with an influx of skilled migrants.

Response to a migration shock

◮ When migrants are more skilled than locals, there is a gain in the average human

capital per worker. Hence the ratio of physical to human capital falls and so does the wage (this is partially offset by the real appreciation).

◮ Because of (a) the appreciation and (b) the increase in the marginal product of

capital, the utilisation rate of installed capital rises. This allows an increase in per capita output even as physical output per head falls.

◮ The increase in utilisation is key to raising output per head. ◮ An increase in net migration raises real house prices and residential investment. ◮ Rise in relative price of houses shifts factors of production out of the goods

producing sector into the construction sector.

◮ This effect is partially offset by an increase in the utilisation rate of installed

capital.

◮ The investment boom and real appreciation lead to a trade deficit.

How important are migration shocks?

Table: Variance decomposition at the posterior mean

Shocks Observables ǫa ǫh ǫyf ǫj ǫi ǫjc ǫv GDP 0.36 0.04 0.00 0.35 0.04 0.02 0.19 [0.22, 0.49] [0.02, 0.06] [0.00, 0.00] [0.12, 0.56] [0.01, 0.07] [0.01, 0.02] [0.11, 0.27] Investment 0.12 0.00 0.00 0.01 0.70 0.00 0.17 [0.05, 0.18] [0.00, 0.00] [0.00, 0.00] [0.00, 0.01] [0.55, 0.85] [0.00, 0.00] [0.07, 0.27] Residential Invest. 0.00 0.46 0.00 0.50 0.00 0.01 0.03 [0.00, 0.00] [0.23, 0.72] [0.00, 0.00] [0.25, 0.76] [0.00, 0.00] [0.00, 0.01] [0.01, 0.04] Consumption 0.24 0.00 0.00 0.02 0.07 0.56 0.12 [0.18, 0.29] [0.00, 0.00] [0.00, 0.00] [0.00, 0.04] [0.04, 0.10] [0.48, 0.62] [0.09, 0.15] Real House Prices 0.05 0.00 0.00 0.88 0.01 0.02 0.04 [0.01, 0.08] [0.00, 0.01] [0.00, 0.00] [0.79, 0.98] [0.00, 0.02] [0.00, 0.03] [0.01, 0.07]

The table reports the theoretical variance decomposition at the posterior mean in percent for the baseline model with migrant human capital in excess of local χ = 1.85. The numbers in brackets are are the 5% and 95% confidence

• intervals. All observables are defined as per data transformations.

How important are migration shocks?

◮ When looked at through the prism of our DSGE model migration shocks matter,

but they are not the key driver of the business cycle for any of our variables.

◮ They account for about 1/5 of the variance of GDP, 17 - 12% of investment and

consumption and no more than 4% for housing market variables.

What about the other shocks?

◮ Predictably, world demand shocks do not matter – the dynamics of the terms of

trade shield the economy from the effects of foreign shocks.

◮ Residential investment is explained in roughly equal proportions by supply and

demand shocks.

◮ House prices are mainly explained by housing demand shocks unrelated to

migration.

◮ Housing demand shocks also affect GDP, as do the usual TFP shocks in the

goods producing sector.

Sensitivity Analysis

◮ To what extent do the results hinge on the relative degree of human capital of

migrants which we could not identify in the data?

◮ Does the general picture hold using a much less restrictive SVAR model?

Sensitivity Analysis - Role of χ

◮ As a sensitivity check, we set χ = 1 which implies that migrants have the same

level of human capital as locals. A priori we would expect to find a reduced role

• f migration.

◮ We find almost an identical set of estimated parameters, yet a much reduced role

• f migration shocks.

Table: Variance decomposition at the posterior mean

Shocks Observables ǫa ǫh ǫyf ǫj ǫi ǫjc ǫv GDP 0.42 0.05 0.00 0.38 0.13 0.01 0.00 [0.25, 0.58] [0.03, 0.08] [0.00, 0.00] [0.16, 0.59] [0.04, 0.22] [0.01, 0.02] [0.00, 0.01] Investment 0.06 0.00 0.00 0.00 0.92 0.00 0.02 [0.02, 0.10] [0.00, 0.00] [0.00, 0.00] [0.00, 0.01] [0.86, 0.97] [0.00, 0.00] [0.00, 0.03]

• Res. Investment

0.00 0.50 0.00 0.48 0.01 0.01 0.01 [0.00, 0.00] [0.27, 0.75] [0.00, 0.00] [0.24, 0.72] [0.00, 0.01] [0.00, 0.01] [0.00, 0.01] Consumption 0.24 0.00 0.00 0.02 0.18 0.53 0.03 [0.18, 0.30] [0.00, 0.00] [0.00, 0.00] [0.00, 0.04] [0.11, 0.26] [0.46, 0.61] [0.02, 0.04] Real House Prices 0.05 0.01 0.00 0.87 0.04 0.02 0.01 [0.01, 0.09] [0.00, 0.02] [0.00, 0.00] [0.77, 0.97] [0.01, 0.07] [0.00, 0.04] [0.00, 0.02]

The table reports the theoretical variance decomposition at the posterior mean in percent for the baseline model with migrant human capital in excess of local χ = 1. The numbers in brackets are are the 5% and 95% confidence

• intervals. All observables are defined as per data transformations.

Sensitivity Analysis - Role of χ

◮ Clearly the type of migrants affects the dynamics of migration shocks. When

migrants have the same level of human capital as locals, migration shocks have no significant business cycle effects.

◮ In this case, migrants are absorbed into the economy with very little aggregate

effects.

◮ If on the other hand, we believe that migration has an effect on the business

cycle, then taking account of migrants’ relative human capital is vital.

◮ The choice of χ affects the estimated model’s variance-covariance matrix and

thus the contribution of migration shocks to the volatility of the data, but it does not really affect the qualitative effects of a migration shock.

Accumulated migration by occupation

• 14000
• 10000
• 6000
• 2000

2000 6000 10000 14000 18000

• 200000
• 120000
• 40000

40000 120000 200000 280000 360000 440000 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008 2013 2018 Construction workers (RHS) All groups (LHS)

Source: Coleman and Karagedikli (RBNZ forthcoming)

◮ Migration focussed on skilled migration from early 1990s.

Qualitative response to a migration shock

◮ A TFP shock is largely insensitive to the specification of the DSGE model, eg a

positive TFP shock expands the components of GDP.

◮ In contrast, the effects of a migration shock are sensitive to specification of the

model.

◮ One way to get a feel for the dynamics of the data is to run a simple SVAR using

the same data that we used to estimate the model.

◮ There is of course no guarantee that a DSGE model and a VAR will give similar

results.

Sensitivity Analysis - Migration in an SVAR

◮ The estimated DSGE model has a lot of structure and the variables we analyse

and data we use are restricted by the number of shocks. A simple VAR allows us the check if the qualitative effects of migration shocks are robust - is an increase in net migration expansionary in per capita terms?

◮ We use a simple Cholesky decomposition that orders world GDP first, net

migration per capita second followed by all other variables. yt = µ + A(L)yt−1 + ut. (22)

◮ We add the real exchange rate and real wages to our dataset.

Figure: A migration shock in a VAR

−.002 .002 .004 −.001 .001 .002 .003 .01 .02 .03 −.01 .01 .02 .0002 .0004 .0006 −.02 −.01 .01 −.01 .01 .02 .03 −.001 .001 .002 10 20 30 40 10 20 30 40 10 20 30 40 Consumption GDP Real House Prices Investment Migration Real Exchange Rate Residential Investment Real Wages

68% CI IRF step

Sensitivity Analysis - Migration in an SVAR

◮ The qualitative response to a migration shock is the same. ◮ An increase in net migration is expansionary for GDP and its components. ◮ Net migration raises residential investment and real house prices. The latter rise

gradually, whereas in our model, the price of housing assets jumps to clear the market on impact.

◮ Consistent with our model, the effective real exchange rate appreciates in

response to an increase in net migration.

◮ The response of real wages to an increase in migration is not significant.

Conclusions / Policy implications

◮ Migration shocks clearly affect the business cycle, but they only explain about

1/5 of the volatility of GDP, which makes them a driver of GDP per capita, but not one of the key drivers such as productivity shocks.

◮ An unexpected increase in net migration is expansionary for the components of

GDP per capita and causes the real exchange rate to appreciate.

◮ The real appreciation creates a positive wealth effects that enhances the marginal

product of factors of production and increase consumption.

◮ An increase in net migration raises both house prices and per capita residential

• investment. Importantly, our model suggests that the increase in residential

investment does not come at the expense of goods production or investment. Key to this result is the endogenous response of utilisation rate of capital.

Conclusions / Policy implications

◮ The relative level of human capital has a material impact on the dynamics of the

model.

◮ Our model suggests that the closer are new migrants to locals in terms of skill

levels, the smaller will the business cycle effects of migration shocks. In the limit when migrants have the same level of human capital and bring with them the average level of productive capital and housing stock, there would be no effect of migration on the business cycle.

◮ Our estimated model is qualitatively consistent with a simple structural VAR

• model. Both the DSGE model and the SVAR suggest that the real exchange rate

appreciates in response to an increase in net migration. Real appreciations are expansionary.

Model details: Households

First order conditions with respect to control variables

jc

t /ct − µt

= 0 (23) −φ0(nt + st)η + µtwt Nt−1 Nt dt−1 = 0 (24) −φ0(nt + st)η + λtφs ( Nt−1

Nt dt−1st)φs

st = 0 (25) −λt + µtwtnt + βEtλt+1  φs (st+1

Nt Nt+1 dt)φ s

dt + (1 − δd) Nt Nt+1   = 0 (26) −µt + βEtµt+1 pf

t+1

pf

t

Nt Nt+1 (1 + rt) = 0 (27) −qH

t + jt

1 (htµt) + βEt Nt Nt+1 µt+1 µt

• (1 − δh)qH

t+1

• = 0

(28) −pl

t + βEt

Nt Nt+1 µt+1 µt

• pl

t+1 + Rl t+1

• = 0

(29)

Take me back

Model details: Goods-producing firms’ first order conditions

◮ The standard optimality condition for effective hours, capital, investment, and

utilisation are: yt eny

t

= wt (30) qt = Etβ Nt Nt+1 µt+1 µt

• ph

t+1

∂yt+1 ∂kt + qt+1(1 − δ(ut+1))

• (31)

1/ai

t = qt

∂ι(xt, xt−1) ∂xt + βEt µt+1 µt qt+1 ∂ι(xt+1, xt) ∂xt

• (32)

. αph

t

yt ut = qtδ′(ut)kt (33)

Take me back